Wireless communication networks of various types use forms of Automatic Repeat reQuest (ARQ) response signaling. With ARQ, transmissions from a given transmitter are acknowledged or not acknowledged, depending on whether they are successfully received. Non-acknowledgments prompt the transmitter to retransmit using, for example, the same channel resources that were allocated for its original transmission.
According to the Long Term Evolution (LTE) standards, as promulgated by the Third Generation Partnership Project (3GPP), LTE networks use Hybrid ARQ (H-ARQ). As an example, given mobile terminals or other types of User Equipment (UE) transmit to an eNodeB in one or more LTE subframes, according to uplink assignment grants made by the eNodeB. An assignment grant allocates particular OFDM channel resources to particular users. Thus, in ongoing operation, the eNodeB receives some number of user signals in each of a series of repeating LTE subframes, and sends ARQ responses to each transmitting user, in dependence on whether that user's signal was successfully received (decoded) by the eNodeB.
In more detail, in 3GPP Release 8, for LTE, an eNodeB sends an H-ARQ response signal on the Physical H-ARQ Indicator Channel (PHICH), wherein an acknowledgment response—sometimes referred to as an “ack”—indicates that the user signal transmitted on the uplink to the eNodeB by a given User Equipment (UE) was successfully decoded. Conversely, a non-acknowledgment response—sometimes referred to as a “nack”—indicates that the user signal was not successfully decoded.
In Frequency-Division Duplexing (FDD) mode, the eNodeB receives some number of user signals in a given LTE subframe, and sends ARQ response signals corresponding to those signals four subframes later, as a PHICH group transmitted on the PHICH. The determination of the PHICH group, as well as the different spreading sequences used to differentiate the different ARQ responses by targeted UEs, is determined based on the locations of the corresponding uplink assignments used for the transmissions being acknowledged. The PHICH is mapped on OFDM symbol “0” for normal durations, or 0, 1, and 2 for extended durations.
To efficiently utilize the available resources, the ARQ signals for up to eight UEs can be multiplexed into a single PHICH group, and there are several such PHICH groups available. The number of PHICH groups depends on the system bandwidth and a semi-static parameter called Ng, to dynamically account for changes in the number of users. There are at least 2 PHICH groups (1.4 MHz and Ng=1/6) and at most 25 (20 MHz and Ng=2) present in the control region of a subframe.
In forming a given PHICH group at the eNodeB, single-bit acks/nacks are coded by a (3, 1) repetition code. To be able to distinguish the different users upon decoding, each UE is assigned a spreading sequence that is orthogonal to the other sequences in a spreading book. Because the spreading factor is four, for the case of normal cyclic prefix, every bit is expanded into four bits, and thus the total number of bits per ack/nack is 12. These bits are mapped onto complex modulation symbols using Binary Phase Shift Keying (BPSK). The fact that the UEs share the energy within one PHICH group allows the eNodeB to carry out power control to balance the decoding performance of the assigned UEs. That is, the eNodeB can allocate ARQ signaling power within the PHICH group in view of the different received signal qualities (e.g., different signal-to-noise ratios or SNRs) at the UEs.
In particular, the eNodeB applies a different amplitude scaling factors to the ARQ signals targeted to different UEs—e.g., for UEs 0 to 7, the eNodeB uses scaling factors G0 to G7 to set the ARQ signal power allocations within the PHICH group, where Gi=√{square root over (Ebi)}.
The resulting signal for transmission of a PHICH group can thus be written as
                              s          =                                    [                                                s                  0                                ⁢                                                                  ⁢                …                ⁢                                                                  ⁢                                  s                  11                                            ]                        T                          ,                                  ⁢        with                            (                  Eq          .                                          ⁢          1                )                                                      s            k                    =                                    ∑                              i                =                0                            7                        ⁢                                                  ⁢                                          G                i                            ·                                                w                  i                                ⁡                                  (                                      k                    ⁢                                                                                  ⁢                    mod                    ⁢                                                                                  ⁢                    4                                    )                                            ·                              ⅇ                                                      jπ                    /                    4                                    -                                      j                    ⁢                                                                                  ⁢                    b                    ⁢                                                                                  ⁢                    π                                                                                      ,                            (                  Eq          .                                          ⁢          2                )            where b maps to ACK (b=1) or NACK (b=0). Note that the sk are mapped onto different resource elements (REs) in the OFDM time-frequency grid of the control region in a given subframe.
For notational simplicity, assume one transmit antenna at the eNodeB and M receiver antennas at the UE. The model of one received RE after the Fast Fourier Transform (FFT) isrk=hk·sk+nk,  (Eq. 3)where rk, hk, and nk are (M×1) column vectors. The channel experienced by RE k is described by hk, and nk CN (0, N0) is a complex Gaussian noise vector and CN is the complex norm. The Maximum Ratio Combining (MRC) solution for sk becomesŝk=hnH·rk=∥hk∥2·sk+hkH·nk,  (Eq. 4)By normalizing with the channel gain, one obtains
                                          s            ^                    k                =                              s            k                    +                                                                      h                  k                  H                                ·                                  n                  k                                                                                                                    h                    k                                                                    2                                      .                                              (                  Eq          .                                          ⁢          5                )            
With knowledge (estimation) of h and the distribution of n, the distribution for the detected symbol ŝ at the UE is
                                          s            ^                    k                ∼                              CN            ⁡                          (                                                s                  k                                ,                                                      N                    0                                                                                                                            h                        k                                                                                    2                                                              )                                .                                    (                  Eq          .                                          ⁢          6                )            The decision variable hi for the decoding the ARQ signal inside a PHICH group, for a specific UE i, over the RE [0, . . . , 11] is derived by
                              hi          =                                    ∑                              k                =                0                            11                        ⁢                                                  ⁢                                          ⅇ                                                      -                    jπ                                    /                  4                                            ·                                                w                  i                  *                                ⁡                                  (                                      k                    ⁢                                                                                  ⁢                    mod                    ⁢                                                                                  ⁢                    4                                    )                                            ·                                                s                  ^                                k                                                    ,                            (                  Eq          .                                          ⁢          7                )            where the rotation is applied to map the received signal onto the real axis. The complex conjugate of the UE's spreading sequence w, is applied to cancel the contribution from the other UEs. For example, for a real spreading sequence, one can write
                    hi        =                              ∑                          k              =              0                        11                    ⁢                      Re            ⁢                                          {                                                      ⅇ                                                                  -                        jπ                                            /                      4                                                        ·                                                            w                      i                      *                                        ⁡                                          (                                              k                        ⁢                                                                                                  ⁢                        mod                        ⁢                                                                                                  ⁢                        4                                            )                                                        ·                                                            s                      ^                                        k                                                  }                            .                                                          (                  Eq          .                                          ⁢          8                )            As such, the UE may take a decision on whether the signal is an ack or a nack according to
                                          b            ^                    i                =                  {                                                                      0                                                                                            if                      ⁢                                                                                          ⁢                      hi                                        ≥                    0                                                                                                1                                                                                            if                      ⁢                                                                                          ⁢                      hi                                        <                    0                                                                        .                                              (                  Eq          .                                          ⁢          9                )            
Notably, however, from a system point of view, there may be different Block Error Rate (BLER) requirements for PHICH decoding, depending on whether an ack or a nack was sent. Consider, for example, the case where, at a given UE, an ack is mistaken for a nack. In this case and if there is not an explicit uplink grant read on the Packet Data Control Channel (PDCCH), the UE will retransmit the apparently non-acknowledged packet using the same uplink resources that were reserved for its original transmission. However, because the eNodeB successfully received the packet, it may have allocated those resources to another UE (or UEs). Thus, the erroneous retransmission, caused by the UE incorrectly interpreting the eNodeB's ack as a nack, causes interference at the eNodeB.
In the other case, the UE mistakes a nack as an ack. This mistake is not as critical from a system standpoint, because the UE simply fails to retransmit and clears its packet buffer; no interference with other uplink transmissions occurs. Of course, a retransmission request has to be taken care of by higher control layers, but these operations only add latency to the retransmission. Therefore, the requirement for Pr{ack→nack} (the probability of ack misinterpreted as nack) is more restrictive than Pr{nack→ack}.
The 3GGP TSG RAN WG 4 defined a test requirement as the smallest SNR where Pr{ack→nack}=10−3 is fulfilled. Accordingly, inside a given PHICH group, power must be distributed such that each UE targeted by the PHICH achieves the probability target. As a reasonable simplification, one may assume that the contributions of the UEs, are decoupled such that the power level of each ARQ signal within a given PHICH group can be set as if no other UE was present.
For a single UE in a PHICH group, from considerations of the probability density functions of a random Gaussian variable, an ack requires almost twice the power to maintain unequal error probabilities, if the decision threshold is located at zero. Given that a UE transmits at a BLER of ten percent, this fact means that acks are sent ninety percent of the time. The likelihood that most or all of the ARQ responses being sent in a given PHICH group will be acknowledgements and the reliability targets for sending those acknowledgments can result in the need for relatively high power allocations at the eNodeB for PHICH group transmissions.